Proper Orthogonal Decomposition
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Multifidelity Proper Orthogonal Decomposition
Announce Type: replace Abstract: This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique for extracting a low-dimensional basis from training data to achieve subsequent dimension reduction or reduced-order modeling. In scientific and engineering applications, the training data are typically numerical snapshot...
Reduced order modeling for spatio-temporal pattern approximation in diffusive Lotka-Volterra equations
arXiv:2606.04030v1 Announce Type: new Abstract: This paper presents an efficient reduced order modeling (ROM) framework for simulating spatio-temporal pattern formation in three-species diffusive Lotka-Volterra systems. To alleviate the high computational cost associated with long-time simulations of the high-dimensional full order model (FOM), we apply proper orthogonal decomposition (POD) to project the solution onto a low-dimensional subspace. Further efficiency is achieved through...
A-priori error estimation for space-time Galerkin POD for linear evolution problems
arXiv:2604.22057v2 Announce Type: replace Abstract: In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only the space dimension but simultaneously the time dimension as well. The proposed a-priori error estimate is developed for a linear parabolic partial differential equation and estimates the error between the...
Leveraging modal structure similarity for simulation of spatially evolving wakes
arXiv:2509.24925v2 Announce Type: replace Abstract: We present a new methodology to enable efficient simulation of high Reynolds number wakes. In this approach, a body-exclusive hybrid simulation at Re = 5 x 10^4 is initialized using inflow fields reconstructed from a lower Reynolds number (Re = 5 x 10^3) body-inclusive simulation. Spectral Proper Orthogonal Decomposition (SPOD) is employed to identify dominant coherent structures, and a low-rank reconstruction generates physically...
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
arXiv:2606.06573v1 Announce Type: cross Abstract: We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The...
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
Announce Type: new Abstract: We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The resulting modes...
Identifying sensitivity-dominant parameters via active subspaces in reduced-order modeling of fluid dynamics
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OnlyDense: Reduced-Order Modeling for Lagrangian simulation
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